Philosophy Lexicon of Arguments

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Adams, R.
 
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Leibniz Principle Millikan I, 261
VsLeibniz' Principle/Law/R. M. Adams/Millikan: Thesis: the principle that is used when such symmetrical worlds are constructed, the principle that an individual cannot be distinguished from itself, so the two world parts of the world cannot be the same half.
Leibniz' law/VsVs/Hacking/Millikan: (recent defense of Hacking): the objections do not consider the fact that this could be about a curved space instead of a doubling.
Curved Space/Hacking/Millikan: here one thing and the same thing emerges again, it is not a doubling as in the Euclidean geometry.
MillikanVsHacking: but that would not answer the question.
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I 262
But there are still two interesting possibilities: > indistinguishability.
Leibniz' Law/Principle/Identity/Indistinguishability/Millikan:
1. symmetrical world: one could argue that there is simply no fact here that decides whether the space is curved or doubled. ((s)> nonfactualism).
N.B.: this would imply that Leibniz' principle is neither metaphysical nor logically necessary, and that its validity is only a matter of convention.
2. Symmetrical world: one could say that the example does not offer a general solution, but the assumption of a certain given symmetrical world: here, there would very well be a fact whether the space is curved or not. A certain given space cannot be both!
N.B.: then Leibniz' principle is neither metaphysical nor logically necessary.
N.B.: but in this case this is not a question of convention, but a real fact!
MillikanVsAdams/MillikanVsArmstrong/Millikan: neither Adams nor Armstrong take that into account.
Curved space/Millikan: here, what is identical is necessarily identical ((s) because it is only mirrored). Here the counterfactual conditional would apply: if the one half had been different, then also the other. Here the space seems to be only doubled.
Doubling/Millikan: if the space (in Euclidean geometry) is mirrored, then the identity is random, but not necessary. Here one half could change without changing the other half. ((s) No counterfactual conditional).
Identity: is given if the objects are not indistinguishable because a law applies in situ, but a natural law, a natural necessity.
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I 263
Then, in the second option, identity is derived from causality.
(x)(y){[NN(F)Fx equi Fy] equi x = y}
NN/Notation: nature-necessary under necessary circumstances.
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Ed. Martin Schulz, access date 2017-03-30